// competitive-verifier: PROBLEM
#include <iostream>
#include <vector>
/**
 * @brief 重み付きグラフ
 *
 * @tparam T 辺の重みの型
 */
template <class T>
struct Graph {
  private:
    struct _edge {
        constexpr _edge() : _from(), _to(), _weight() {}
        constexpr _edge(int from, int to, T weight) : _from(from), _to(to), _weight(weight) {}
        constexpr bool operator<(const _edge &rhs) const { return weight() < rhs.weight(); }
        constexpr bool operator>(const _edge &rhs) const { return rhs < *this; }
        constexpr int from() const { return _from; }
        constexpr int to() const { return _to; }
        constexpr T weight() const { return _weight; }
      private:
        int _from, _to;
        T _weight;
    };
  public:
    using edge_type = typename Graph<T>::_edge;
    Graph() : _size(), edges() {}
    Graph(int v) : _size(v), edges(v) {}
    const auto &operator[](int i) const { return edges[i]; }
    auto &operator[](int i) { return edges[i]; }
    const auto begin() const { return edges.begin(); }
    auto begin() { return edges.begin(); }
    const auto end() const { return edges.end(); }
    auto end() { return edges.end(); }
    constexpr int size() const { return _size; }
    void add_edge(const edge_type &e) { edges[e.from()].emplace_back(e); }
    void add_edge(int from, int to, T weight = T(1)) { edges[from].emplace_back(from, to, weight); }
    void add_edges(int from, int to, T weight = T(1)) {
        edges[from].emplace_back(from, to, weight);
        edges[to].emplace_back(to, from, weight);
    }
    void input_edge(int m, int base = 1) {
        for (int i = 0; i < m; ++i) {
            int from, to;
            T weight;
            std::cin >> from >> to >> weight;
            add_edge(from - base, to - base, weight);
        }
    }
    void input_edges(int m, int base = 1) {
        for (int i = 0; i < m; ++i) {
            int from, to;
            T weight;
            std::cin >> from >> to >> weight;
            add_edges(from - base, to - base, weight);
        }
    }
  private:
    int _size;
    std::vector<std::vector<edge_type>> edges;
};
template <>
struct Graph<void> {
  private:
    struct _edge {
        constexpr _edge() : _from(), _to() {}
        constexpr _edge(int from, int to) : _from(from), _to(to) {}
        constexpr int from() const { return _from; }
        constexpr int to() const { return _to; }
        constexpr int weight() const { return 1; }
        constexpr bool operator<(const _edge &rhs) const { return weight() < rhs.weight(); }
        constexpr bool operator>(const _edge &rhs) const { return rhs < *this; }
      private:
        int _from, _to;
    };
  public:
    using edge_type = typename Graph<void>::_edge;
    Graph() : _size(), edges() {}
    Graph(int v) : _size(v), edges(v) {}
    const auto &operator[](int i) const { return edges[i]; }
    auto &operator[](int i) { return edges[i]; }
    const auto begin() const { return edges.begin(); }
    auto begin() { return edges.begin(); }
    const auto end() const { return edges.end(); }
    auto end() { return edges.end(); }
    constexpr int size() const { return _size; }
    void add_edge(const edge_type &e) { edges[e.from()].emplace_back(e); }
    void add_edge(int from, int to) { edges[from].emplace_back(from, to); }
    void add_edges(int from, int to) {
        edges[from].emplace_back(from, to);
        edges[to].emplace_back(to, from);
    }
    void input_edge(int m, int base = 1) {
        for (int i = 0; i < m; ++i) {
            int from, to;
            std::cin >> from >> to;
            add_edge(from - base, to - base);
        }
    }
    void input_edges(int m, int base = 1) {
        for (int i = 0; i < m; ++i) {
            int from, to;
            std::cin >> from >> to;
            add_edges(from - base, to - base);
        }
    }
  private:
    int _size;
    std::vector<std::vector<edge_type>> edges;
};
#include <cstdint>
#include <type_traits>
#include <utility>
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr std::int64_t safe_mod(std::int64_t x, std::int64_t m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    std::uint64_t im;
    // @param m `1 <= m`
    explicit barrett(unsigned int m) : _m(m), im((std::uint64_t)(-1) / m + 1) {}
    // @return m
    unsigned int umod() const { return _m; }
    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        std::uint64_t z = a;
        z *= b;
        std::uint64_t x = (std::uint64_t)(((__uint128_t)(z)*im) >> 64);
        std::uint64_t y = x * _m;
        return (unsigned int)(z - y + (z < y ? _m : 0));
    }
};
struct montgomery {
    std::uint64_t _m;
    std::uint64_t im;
    std::uint64_t r2;
    // @param m `1 <= m`
    explicit constexpr montgomery(std::uint64_t m) : _m(m), im(m), r2(-__uint128_t(m) % m) {
        for (int i = 0; i < 5; ++i) im = im * (2 - _m * im);
        im = -im;
    }
    // @return m
    constexpr std::uint64_t umod() const { return _m; }
    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    constexpr std::uint64_t mul(std::uint64_t a, std::uint64_t b) const { return mr(mr(a, b), r2); }
    constexpr std::uint64_t exp(std::uint64_t a, std::uint64_t b) const {
        std::uint64_t res = 1, p = mr(a, r2);
        while (b) {
            if (b & 1) res = mr(res, p);
            p = mr(p, p);
            b >>= 1;
        }
        return res;
    }
    constexpr bool same_pow(std::uint64_t x, int s, std::uint64_t n) const {
        x = mr(x, r2), n = mr(n, r2);
        for (int r = 0; r < s; r++) {
            if (x == n) return true;
            x = mr(x, x);
        }
        return false;
    }
  private:
    constexpr std::uint64_t mr(std::uint64_t x) const {
        return ((__uint128_t)(x * im) * _m + x) >> 64;
    }
    constexpr std::uint64_t mr(std::uint64_t a, std::uint64_t b) const {
        __uint128_t t = (__uint128_t)a * b;
        std::uint64_t inc = std::uint64_t(t) != 0;
        std::uint64_t x = t >> 64, y = ((__uint128_t)(a * b * im) * _m) >> 64;
        unsigned long long z = 0;
        bool f = __builtin_uaddll_overflow(x, y, &z);
        z += inc;
        return f ? z - _m : z;
    }
};
constexpr bool is_SPRP32(std::uint32_t n, std::uint32_t a) {
    std::uint32_t d = n - 1, s = 0;
    while ((d & 1) == 0) ++s, d >>= 1;
    std::uint64_t cur = 1, pw = d;
    while (pw) {
        if (pw & 1) cur = (cur * a) % n;
        a = (std::uint64_t)a * a % n;
        pw >>= 1;
    }
    if (cur == 1) return true;
    for (std::uint32_t r = 0; r < s; r++) {
        if (cur == n - 1) return true;
        cur = cur * cur % n;
    }
    return false;
}
// given 2 <= n,a < 2^64, a prime, check whether n is a-SPRP
constexpr bool is_SPRP64(const montgomery &m, std::uint64_t a) {
    auto n = m.umod();
    if (n == a) return true;
    if (n % a == 0) return false;
    std::uint64_t d = n - 1;
    int s = 0;
    while ((d & 1) == 0) ++s, d >>= 1;
    std::uint64_t cur = m.exp(a, d);
    if (cur == 1) return true;
    return m.same_pow(cur, s, n - 1);
}
constexpr bool is_prime_constexpr(std::uint64_t x) {
    if (x == 2 || x == 3 || x == 5 || x == 7) return true;
    if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0) return false;
    if (x < 121) return (x > 1);
    montgomery m(x);
    constexpr std::uint64_t bases[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
    for (auto a : bases) {
        if (!is_SPRP64(m, a)) return false;
    }
    return true;
}
constexpr bool is_prime_constexpr(std::int64_t x) {
    if (x < 0) return false;
    return is_prime_constexpr(std::uint64_t(x));
}
constexpr bool is_prime_constexpr(std::uint32_t x) {
    if (x == 2 || x == 3 || x == 5 || x == 7) return true;
    if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0) return false;
    if (x < 121) return (x > 1);
    std::uint64_t h = x;
    h = ((h >> 16) ^ h) * 0x45d9f3b;
    h = ((h >> 16) ^ h) * 0x45d9f3b;
    h = ((h >> 16) ^ h) & 255;
    constexpr uint16_t bases[] = {
        15591, 2018,  166,   7429,  8064,  16045, 10503, 4399,  1949,  1295,  2776,  3620,  560,
        3128,  5212,  2657,  2300,  2021,  4652,  1471,  9336,  4018,  2398,  20462, 10277, 8028,
        2213,  6219,  620,   3763,  4852,  5012,  3185,  1333,  6227,  5298,  1074,  2391,  5113,
        7061,  803,   1269,  3875,  422,   751,   580,   4729,  10239, 746,   2951,  556,   2206,
        3778,  481,   1522,  3476,  481,   2487,  3266,  5633,  488,   3373,  6441,  3344,  17,
        15105, 1490,  4154,  2036,  1882,  1813,  467,   3307,  14042, 6371,  658,   1005,  903,
        737,   1887,  7447,  1888,  2848,  1784,  7559,  3400,  951,   13969, 4304,  177,   41,
        19875, 3110,  13221, 8726,  571,   7043,  6943,  1199,  352,   6435,  165,   1169,  3315,
        978,   233,   3003,  2562,  2994,  10587, 10030, 2377,  1902,  5354,  4447,  1555,  263,
        27027, 2283,  305,   669,   1912,  601,   6186,  429,   1930,  14873, 1784,  1661,  524,
        3577,  236,   2360,  6146,  2850,  55637, 1753,  4178,  8466,  222,   2579,  2743,  2031,
        2226,  2276,  374,   2132,  813,   23788, 1610,  4422,  5159,  1725,  3597,  3366,  14336,
        579,   165,   1375,  10018, 12616, 9816,  1371,  536,   1867,  10864, 857,   2206,  5788,
        434,   8085,  17618, 727,   3639,  1595,  4944,  2129,  2029,  8195,  8344,  6232,  9183,
        8126,  1870,  3296,  7455,  8947,  25017, 541,   19115, 368,   566,   5674,  411,   522,
        1027,  8215,  2050,  6544,  10049, 614,   774,   2333,  3007,  35201, 4706,  1152,  1785,
        1028,  1540,  3743,  493,   4474,  2521,  26845, 8354,  864,   18915, 5465,  2447,  42,
        4511,  1660,  166,   1249,  6259,  2553,  304,   272,   7286,  73,    6554,  899,   2816,
        5197,  13330, 7054,  2818,  3199,  811,   922,   350,   7514,  4452,  3449,  2663,  4708,
        418,   1621,  1171,  3471,  88,    11345, 412,   1559,  194};
    return is_SPRP32(x, bases[h]);
}
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr std::int64_t pow_mod_constexpr(std::int64_t x, std::int64_t n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    std::uint64_t r = 1;
    std::uint64_t y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    std::int64_t d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr std::int64_t bases[3] = {2, 7, 61};
    for (std::int64_t a : bases) {
        std::int64_t t = d;
        std::int64_t y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) { return false; }
    }
    return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<std::int64_t, std::int64_t> inv_gcd(std::int64_t a, std::int64_t b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};
    std::int64_t s = b, t = a;
    std::int64_t m0 = 0, m1 = 1;
    while (t) {
        std::int64_t u = s / t;
        s -= t * u;
        m0 -= m1 * u;
        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (std::int64_t)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) { x /= i; }
        }
    }
    if (x > 1) { divs[cnt++] = x; }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m>
constexpr int primitive_root = primitive_root_constexpr(m);
}  // namespace internal
#include <cassert>
#include <numeric>
namespace internal {
template <class T>
using is_signed_int128 = typename std::conditional<std::is_same<T, __int128_t>::value ||
                                                       std::is_same<T, __int128>::value,
                                                   std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int128 = typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                                         std::is_same<T, unsigned __int128>::value,
                                                     std::true_type, std::false_type>::type;
template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>;
template <class T>
using is_integral =
    typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using is_signed_int =
    typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) ||
                                  is_signed_int128<T>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value, make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T>
using to_unsigned_t = typename to_unsigned<T>::type;
}  // namespace internal
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T>
using is_modint = std::is_base_of<modint_base, T>;
template <class T>
using is_modint_t = std::enable_if_t<is_modint<T>::value>;
}  // namespace internal
template <int m, std::enable_if_t<(1 <= m)> * = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;
  public:
    static constexpr int mod() { return m; }
    static constexpr mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    constexpr static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T> * = nullptr>
    constexpr static_modint(T v) : _v(0) {
        std::int64_t x = (std::int64_t)(v % (std::int64_t)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T> * = nullptr>
    constexpr static_modint(T v) : _v(0) {
        _v = (unsigned int)(v % umod());
    }
    constexpr unsigned int val() const { return _v; }
    constexpr mint &operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    constexpr mint &operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    constexpr mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    constexpr mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    constexpr mint &operator+=(const mint &rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    constexpr mint &operator-=(const mint &rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    constexpr mint &operator*=(const mint &rhs) {
        std::uint64_t z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    constexpr mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }
    constexpr mint operator+() const { return *this; }
    constexpr mint operator-() const { return mint() - *this; }
    constexpr mint pow(std::int64_t n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    constexpr mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    friend constexpr mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
    friend constexpr mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
    friend constexpr mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
    friend constexpr mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
    friend constexpr bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
    friend constexpr bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
    friend std::istream &operator>>(std::istream &is, mint &rhs) {
        std::int64_t t;
        is >> t;
        rhs = mint(t);
        return is;
    }
    friend constexpr std::ostream &operator<<(std::ostream &os, const mint &rhs) {
        return os << rhs._v;
    }
  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};
template <int id>
struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;
  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T> * = nullptr>
    dynamic_modint(T v) {
        std::int64_t x = (std::int64_t)(v % (std::int64_t)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T> * = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }
    unsigned int val() const { return _v; }
    mint &operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint &operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    mint &operator+=(const mint &rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint &operator-=(const mint &rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint &operator*=(const mint &rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint pow(std::int64_t n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }
    friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
    friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
    friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
    friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
    friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
    friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
    friend std::istream &operator>>(std::istream &is, mint &rhs) {
        std::int64_t t;
        is >> t;
        rhs = mint(t);
        return is;
    }
    friend constexpr std::ostream &operator<<(std::ostream &os, const mint &rhs) {
        return os << rhs._v;
    }
  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id>
internal::barrett dynamic_modint<id>::bt(998244353);
using modint998 = static_modint<998244353>;
using modint107 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class>
struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
}  // namespace internal
namespace internal {
// @return same with std::bit::bit_ceil
unsigned int bit_ceil(unsigned int n) {
    unsigned int x = 1;
    while (x < (unsigned int)(n)) x *= 2;
    return x;
}
// @param n `1 <= n`
// @return same with std::bit::countl_zero
int countl_zero(unsigned int n) { return __builtin_clz(n); }
// @param n `1 <= n`
// @return same with std::bit::countr_zero
int countr_zero(unsigned int n) { return __builtin_ctz(n); }
// @param n `1 <= n`
// @return same with std::bit::countr_zero
constexpr int countr_zero_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}
}  // namespace internal
#include <algorithm>
#include <limits>
template <class T>
struct Add {
    using value_type = T;
    static constexpr T id() { return T(); }
    static constexpr T op(const T &lhs, const T &rhs) { return lhs + rhs; }
    template <class U>
    static constexpr U f(T lhs, U rhs) {
        return lhs + rhs;
    }
};
template <class T>
struct Mul {
    using value_type = T;
    static constexpr T id() { return T(1); }
    static constexpr T op(const T &lhs, const T &rhs) { return lhs * rhs; }
    template <class U>
    static constexpr U f(T lhs, U rhs) {
        return lhs * rhs;
    }
};
template <class T>
struct And {
    using value_type = T;
    static constexpr T id() { return std::numeric_limits<T>::max(); }
    static constexpr T op(const T &lhs, const T &rhs) { return lhs & rhs; }
    template <class U>
    static constexpr U f(T lhs, U rhs) {
        return lhs & rhs;
    }
};
template <class T>
struct Or {
    using value_type = T;
    static constexpr T id() { return T(); }
    static constexpr T op(const T &lhs, const T &rhs) { return lhs | rhs; }
    template <class U>
    static constexpr U f(T lhs, U rhs) {
        return lhs | rhs;
    }
};
template <class T>
struct Xor {
    using value_type = T;
    static constexpr T id() { return T(); }
    static constexpr T op(const T &lhs, const T &rhs) { return lhs ^ rhs; }
    template <class U>
    static constexpr U f(T lhs, U rhs) {
        return lhs ^ rhs;
    }
};
template <class T>
struct Min {
    using value_type = T;
    static constexpr T id() { return std::numeric_limits<T>::max(); }
    static constexpr T op(const T &lhs, const T &rhs) { return std::min(lhs, rhs); }
    template <class U>
    static constexpr U f(T lhs, U rhs) {
        return std::min((U)lhs, rhs);
    }
};
template <class T>
struct Max {
    using value_type = T;
    static constexpr T id() { return std::numeric_limits<T>::lowest(); }
    static constexpr T op(const T &lhs, const T &rhs) { return std::max(lhs, rhs); }
    template <class U>
    static constexpr U f(T lhs, U rhs) {
        return std::max((U)lhs, rhs);
    }
};
template <class T>
struct Gcd {
    using value_type = T;
    static constexpr T id() { return std::numeric_limits<T>::max(); }
    static constexpr T op(const T &lhs, const T &rhs) {
        return lhs == Gcd::id() ? rhs : (rhs == Gcd::id() ? lhs : std::gcd(lhs, rhs));
    }
};
template <class T>
struct Lcm {
    using value_type = T;
    static constexpr T id() { return std::numeric_limits<T>::max(); }
    static constexpr T op(const T &lhs, const T &rhs) {
        return lhs == Lcm::id() ? rhs : (rhs == Lcm::id() ? lhs : std::lcm(lhs, rhs));
    }
};
template <class T>
struct Update {
    using value_type = T;
    static constexpr T id() { return std::numeric_limits<T>::max(); }
    static constexpr T op(const T &lhs, const T &rhs) { return lhs == Update::id() ? rhs : lhs; }
    template <class U>
    static constexpr U f(T lhs, U rhs) {
        return lhs == Update::id() ? rhs : lhs;
    }
};
template <class T>
struct Affine {
    using P = std::pair<T, T>;
    using value_type = P;
    static constexpr P id() { return P(1, 0); }
    static constexpr P op(P lhs, P rhs) {
        return {lhs.first * rhs.first, lhs.first * rhs.second + lhs.second};
    }
};
template <class M>
struct Rev {
    using T = typename M::value_type;
    using value_type = T;
    static constexpr T id() { return M::id(); }
    static constexpr T op(T lhs, T rhs) { return M::op(rhs, lhs); }
};
/**
 * @brief 遅延評価セグメント木
 * @see https://github.com/atcoder/ac-library/blob/master/atcoder/lazysegtree.hpp
 *
 * @tparam S モノイド
 * @tparam F モノイド
 */
template <class S, class F>
struct lazy_segment_tree {
  private:
    using T = typename S::value_type;
    using U = typename F::value_type;
  public:
    lazy_segment_tree() : lazy_segment_tree(0) {}
    explicit lazy_segment_tree(int n, T e = S::id()) : lazy_segment_tree(std::vector<T>(n, e)) {}
    explicit lazy_segment_tree(const std::vector<T> &v) : _n(int(v.size())) {
        _size = internal::bit_ceil(_n);
        _log = internal::countr_zero(_size);
        data = std::vector<T>(2 * _size, S::id());
        lazy = std::vector<U>(_size, F::id());
        for (int i = 0; i < _n; i++) data[_size + i] = v[i];
        for (int i = _size - 1; i >= 1; --i) update(i);
    }
    void set(int p, T x) {
        assert(0 <= p && p < _n);
        p += _size;
        for (int i = _log; i >= 1; --i) push(p >> i);
        data[p] = x;
        for (int i = 1; i <= _log; ++i) update(p >> i);
    }
    T at(int p) { return get(p); }
    T get(int p) {
        assert(0 <= p && p < _n);
        p += _size;
        for (int i = _log; i >= 1; --i) push(p >> i);
        return data[p];
    }
    void apply(int p, U f) {
        assert(0 <= p && p < _n);
        p += _size;
        for (int i = _log; i >= 1; --i) push(p >> i);
        data[p] = F::f(f, data[p]);
        for (int i = 1; i <= _log; ++i) update(p >> i);
    }
    void apply(int l, int r, U f) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return;
        l += _size, r += _size;
        for (int i = _log; i >= 1; --i) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }
        int l2 = l, r2 = r;
        while (l < r) {
            if (l & 1) all_apply(l++, f);
            if (r & 1) all_apply(--r, f);
            l >>= 1, r >>= 1;
        }
        l = l2, r = r2;
        for (int i = 1; i <= _log; i++) {
            if (((l >> i) << i) != l) update(l >> i);
            if (((r >> i) << i) != r) update((r - 1) >> i);
        }
    }
    T prod(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return S::id();
        l += _size, r += _size;
        for (int i = _log; i >= 1; --i) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }
        T sml = S::id(), smr = S::id();
        while (l < r) {
            if (l & 1) sml = S::op(sml, data[l++]);
            if (r & 1) smr = S::op(data[--r], smr);
            l >>= 1, r >>= 1;
        }
        return S::op(sml, smr);
    }
    T all_prod() const { return data[1]; }
    int max_right(int l, T val) {
        auto f = [&val](T v) { return !(val < v); };
        return max_right(l, f);
    }
    template <class G>
    int max_right(int l, G g) {
        assert(0 <= l && l <= _n);
        assert(g(S::id()));
        if (l == _n) return _n;
        l += _size;
        for (int i = _log; i >= 1; i--) push(l >> i);
        T sm = S::id();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!g(S::op(sm, data[l]))) {
                while (l < _size) {
                    push(l);
                    l = (2 * l);
                    if (g(S::op(sm, data[l]))) {
                        sm = S::op(sm, data[l]);
                        l++;
                    }
                }
                return l - _size;
            }
            sm = S::op(sm, data[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }
    int min_left(int l, T val) {
        auto f = [&val](T v) { return !(val < v); };
        return min_left(l, f);
    }
    template <class G>
    int min_left(int r, G g) {
        assert(0 <= r && r <= _n);
        assert(g(S::id()));
        if (r == 0) return 0;
        r += _size;
        for (int i = _log; i >= 1; i--) push((r - 1) >> i);
        S sm = S::id();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!g(S::op(data[r], sm))) {
                while (r < _size) {
                    push(r);
                    r = (2 * r + 1);
                    if (g(S::op(data[r], sm))) {
                        sm = S::op(data[r], sm);
                        r--;
                    }
                }
                return r + 1 - _size;
            }
            sm = S::op(data[r], sm);
        } while ((r & -r) != r);
        return 0;
    }
  private:
    int _n, _size, _log;
    std::vector<T> data;
    std::vector<U> lazy;
    void update(int k) { data[k] = S::op(data[2 * k], data[2 * k + 1]); }
    void all_apply(int k, U f) {
        data[k] = F::f(f, data[k]);
        if (k < _size) lazy[k] = F::op(f, lazy[k]);
    }
    void push(int k) {
        all_apply(2 * k, lazy[k]);
        all_apply(2 * k + 1, lazy[k]);
        lazy[k] = F::id();
    }
};
#ifdef ATCODER
#pragma GCC target("sse4.2,avx512f,avx512dq,avx512ifma,avx512cd,avx512bw,avx512vl,bmi2")
#endif
#pragma GCC optimize("Ofast,fast-math,unroll-all-loops")
#include <bits/stdc++.h>
#ifndef ATCODER
#pragma GCC target("sse4.2,avx2,bmi2")
#endif
template <class T, class U>
constexpr bool chmax(T &a, const U &b) {
    return a < (T)b ? a = (T)b, true : false;
}
template <class T, class U>
constexpr bool chmin(T &a, const U &b) {
    return (T)b < a ? a = (T)b, true : false;
}
constexpr std::int64_t INF = 1000000000000000003;
constexpr int Inf = 1000000003;
constexpr double EPS = 1e-7;
constexpr double PI = 3.14159265358979323846;
#define FOR(i, m, n) for (int i = (m); i < int(n); ++i)
#define FORR(i, m, n) for (int i = (m)-1; i >= int(n); --i)
#define FORL(i, m, n) for (int64_t i = (m); i < int64_t(n); ++i)
#define rep(i, n) FOR (i, 0, n)
#define repn(i, n) FOR (i, 1, n + 1)
#define repr(i, n) FORR (i, n, 0)
#define repnr(i, n) FORR (i, n + 1, 1)
#define all(s) (s).begin(), (s).end()
struct Sonic {
    Sonic() {
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
        std::cout << std::fixed << std::setprecision(20);
    }
    constexpr void operator()() const {}
} sonic;
using namespace std;
using ll = std::int64_t;
using ld = long double;
template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
    return is >> p.first >> p.second;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
    for (T &i : v) is >> i;
    return is;
}
template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
    return os << '(' << p.first << ',' << p.second << ')';
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
    for (auto it = v.begin(); it != v.end(); ++it) os << (it == v.begin() ? "" : " ") << *it;
    return os;
}
template <class Head, class... Tail>
void co(Head &&head, Tail &&...tail) {
    if constexpr (sizeof...(tail) == 0) std::cout << head << '\n';
    else std::cout << head << ' ', co(std::forward<Tail>(tail)...);
}
template <class Head, class... Tail>
void ce(Head &&head, Tail &&...tail) {
    if constexpr (sizeof...(tail) == 0) std::cerr << head << '\n';
    else std::cerr << head << ' ', ce(std::forward<Tail>(tail)...);
}
void Yes(bool is_correct = true) { std::cout << (is_correct ? "Yes\n" : "No\n"); }
void No(bool is_not_correct = true) { Yes(!is_not_correct); }
void YES(bool is_correct = true) { std::cout << (is_correct ? "YES\n" : "NO\n"); }
void NO(bool is_not_correct = true) { YES(!is_not_correct); }
void Takahashi(bool is_correct = true) { std::cout << (is_correct ? "Takahashi" : "Aoki") << '\n'; }
void Aoki(bool is_not_correct = true) { Takahashi(!is_not_correct); }
namespace internal {
struct graph_csr {
  private:
    struct edge_list {
        using const_iterator = std::vector<int>::const_iterator;
        edge_list(const graph_csr &g, int v) : g(g), v(v) {}
        const_iterator begin() const { return std::next(g.elist.begin(), g.start[v]); }
        const_iterator end() const { return std::next(g.elist.begin(), g.start[v + 1]); }
      private:
        const graph_csr &g;
        int v;
    };
  public:
    graph_csr(int n) : _size(n), edges(), start(n + 1) {}
    edge_list operator[](int i) const { return edge_list(*this, i); }
    constexpr int size() const { return _size; }
    void build() {
        for (auto [u, v] : edges) ++start[u + 1];
        for (int i = 0; i < _size; ++i) start[i + 1] += start[i];
        auto counter = start;
        elist = std::vector<int>(edges.size());
        for (auto [u, v] : edges) elist[counter[u]++] = v;
    }
    void add_edge(int u, int v) { edges.emplace_back(u, v); }
    void add_edges(int u, int v) {
        edges.emplace_back(u, v);
        edges.emplace_back(v, u);
    }
    void input_edge(int m, int base = 1) {
        for (int i = 0; i < m; ++i) {
            int from, to;
            std::cin >> from >> to;
            add_edge(from - base, to - base);
        }
        build();
    }
    void input_edges(int m, int base = 1) {
        for (int i = 0; i < m; ++i) {
            int from, to;
            std::cin >> from >> to;
            add_edges(from - base, to - base);
        }
        build();
    }
    int _size;
    std::vector<std::pair<int, int>> edges;
    std::vector<int> elist;
    std::vector<int> start;
};
}  // namespace internal
/**
 * @brief HL分解
 * @see https://beet-aizu.github.io/library/tree/heavylightdecomposition.cpp
 */
struct heavy_light_decomposition {
    heavy_light_decomposition() = default;
    template <class T>
    heavy_light_decomposition(const Graph<T> &g, int r = 0) : heavy_light_decomposition(g.size()) {
        std::vector<int> heavy_path(_size, -1), sub_size(_size, 1);
        std::stack<int> st;
        st.emplace(r);
        int pos = 0;
        while (!st.empty()) {
            int v = st.top();
            st.pop();
            vid[pos++] = v;
            for (auto &e : g[v]) {
                int u = e.to();
                if (u == par[v]) continue;
                par[u] = v, dep[u] = dep[v] + 1, st.emplace(u);
            }
        }
        for (int i = _size - 1; i >= 0; --i) {
            int v = vid[i];
            int max_sub = 0;
            for (auto &e : g[v]) {
                int u = e.to();
                if (u == par[v]) continue;
                sub_size[v] += sub_size[u];
                if (max_sub < sub_size[u]) max_sub = sub_size[u], heavy_path[v] = u;
            }
        }
        nxt[r] = r;
        pos = 0;
        st.emplace(r);
        while (!st.empty()) {
            int v = st.top();
            st.pop();
            vid[v] = pos++;
            inv[vid[v]] = v;
            int hp = heavy_path[v];
            for (auto &e : g[v]) {
                int u = e.to();
                if (u == par[v] || u == hp) continue;
                nxt[u] = u, st.emplace(u);
            }
            if (hp != -1) nxt[hp] = nxt[v], st.emplace(hp);
        }
    }
    heavy_light_decomposition(const internal::graph_csr &g, int r = 0)
        : heavy_light_decomposition(g.size()) {
        std::vector<int> heavy_path(_size, -1), sub_size(_size, 1);
        std::stack<int> st;
        st.emplace(r);
        int pos = 0;
        while (!st.empty()) {
            int v = st.top();
            st.pop();
            vid[pos++] = v;
            for (int u : g[v]) {
                if (u == par[v]) continue;
                par[u] = v, dep[u] = dep[v] + 1, st.emplace(u);
            }
        }
        for (int i = _size - 1; i >= 0; --i) {
            int v = vid[i];
            int max_sub = 0;
            for (int u : g[v]) {
                if (u == par[v]) continue;
                sub_size[v] += sub_size[u];
                if (max_sub < sub_size[u]) max_sub = sub_size[u], heavy_path[v] = u;
            }
        }
        nxt[r] = r;
        pos = 0;
        st.emplace(r);
        while (!st.empty()) {
            int v = st.top();
            st.pop();
            vid[v] = pos++;
            inv[vid[v]] = v;
            int hp = heavy_path[v];
            for (int u : g[v]) {
                if (u == par[v] || u == hp) continue;
                nxt[u] = u, st.emplace(u);
            }
            if (hp != -1) nxt[hp] = nxt[v], st.emplace(hp);
        }
    }
    constexpr int size() const { return _size; }
    int get(int v) const { return vid[v]; }
    int get_parent(int v) const { return par[v]; }
    int get_depth(int v) const { return dep[v]; }
    int dist(int u, int v) const {
        int d = 0;
        while (true) {
            if (vid[u] > vid[v]) std::swap(u, v);
            if (nxt[u] == nxt[v]) return d + vid[v] - vid[u];
            d += vid[v] - vid[nxt[v]] + 1;
            v = par[nxt[v]];
        }
    }
    int jump(int u, int v, int k) const {
        int d = dist(u, v);
        if (d < k) return -1;
        int l = lca(u, v);
        if (dist(u, l) >= k) return la(u, k);
        else return la(v, d - k);
    }
    int la(int v, int k) const {
        while (true) {
            int u = nxt[v];
            if (vid[v] - k >= vid[u]) return inv[vid[v] - k];
            k -= vid[v] - vid[u] + 1;
            v = par[u];
        }
    }
    int lca(int u, int v) const {
        while (true) {
            if (vid[u] > vid[v]) std::swap(u, v);
            if (nxt[u] == nxt[v]) return u;
            v = par[nxt[v]];
        }
    }
    template <class F>
    void for_each(int u, int v, const F &f) const {
        while (true) {
            if (vid[u] > vid[v]) std::swap(u, v);
            f(std::max(vid[nxt[v]], vid[u]), vid[v] + 1);
            if (nxt[u] != nxt[v]) v = par[nxt[v]];
            else break;
        }
    }
    template <class F>
    void for_each_edge(int u, int v, const F &f) const {
        while (true) {
            if (vid[u] > vid[v]) std::swap(u, v);
            if (nxt[u] != nxt[v]) {
                f(vid[nxt[v]], vid[v] + 1);
                v = par[nxt[v]];
            } else {
                if (u != v) f(vid[u] + 1, vid[v] + 1);
                break;
            }
        }
    }
  private:
    int _size;
    std::vector<int> vid, nxt, par, dep, inv;
    heavy_light_decomposition(int n) : _size(n), vid(n, -1), nxt(n), par(n, -1), dep(n), inv(n) {}
};
using Mint = modint107;
struct S {
    Mint x, y;
    S operator+(const S &rhs) const {
        return S{x + rhs.x, y + rhs.y};
    }
};
struct F {
    Mint x;
    F operator+(const F &rhs) const {
        return F{x + rhs.x};
    }
    S operator+(const S &rhs) const {
        return S{rhs.x + x * rhs.y, rhs.y};
    }
};
int main(void) {
    int n;
    cin >> n;
    vector<int> s(n), c(n);
    cin >> s >> c;
    Graph<void> g(n);
    g.input_edges(n - 1);
    heavy_light_decomposition hld(g);
    vector<S> v(n);
    rep (i, n) v[hld.get(i)] = {s[i], c[i]};
    lazy_segment_tree<Add<S>, Add<F>> seg(v);
    int q;
    cin >> q;
    while (q--) {
        int t;
        cin >> t;
        if (t == 0) {
            int x, y, z;
            cin >> x >> y >> z;
            --x, --y;
            auto f = [&](int u, int v) {
                seg.apply(u, v, F{z});
            };
            hld.for_each(x, y, f);
        } else {
            int x, y;
            cin >> x >> y;
            --x, --y;
            Mint ans = 0;
            auto f = [&](int u, int v) {
                ans += seg.prod(u, v).x;
            };
            hld.for_each(x, y, f);
            co(ans);
        }
    }
    return 0;
}